Failure Strength Tests

Abstract

Failure strength tests are used for quality control, for adhesive properties development, and for design purposes. Typically, manufacturers provide the average single lap joint (SLJ) shear strength and the peel strength. However, these are not intrinsic adhesive properties and are of limited use for design purposes. The prediction of the joint strength based on stress or strain limit criteria needs the adhesive stress–strain curve. In this chapter, the most important tests for the determination of the adhesive mechanical properties are described. Tests for the three basic loading modes – tension, compression, and shear – are discussed, indicating for each case the advantages and disadvantages. Reference is made to the corresponding standards according to the major standards-setting organizations such as the American Society for Testing and Materials (ASTM) and the International Standards Organization (ISO). Within each category (compression, tension, and shear), tests on bulk specimens and those on joints are compared. Recommendations to select the most suitable test are given, and it is shown that a reasonable relationship exists between adhesive properties measured in compression, tension, and shear.

1 Introduction

Failure strength tests are carried out for different purposes. During the formulation and development stage, manufacturers need to certify their products, and the commonly used tests are failure strength tests. These can be related to the application for which the adhesive is designed using loadings and adherends found in a particular application. Also, some manufacturers provide standard tests that are universal and can be used not only for qualitative but also for design purposes. In many cases, manufacturers provide limited information in the adhesive data sheet, and it is therefore necessary for the joint designer or the researcher to carefully test the adhesive properties. There is a wide variety of standard tests available in different countries (USA, Britain, France, Germany, and Japan) that are also provided by many organizations at the international level, such as the International Standards Organization (ISO) and the European Standards (EN) Organization. Wherever available, adhesive testing standards from these organizations and others are given in this chapter.

When a complex joint is to be introduced in a structure, the ideal situation is to test that specific joint. However, this approach is very expensive. Before real joints or prototypes are built, the designer should first come up with a good prediction of the failure load based, among other things, on the basic mechanical properties of the adhesive. The basic properties can mean the elastic properties, such as the Young’s modulus and the Poisson’s ratio in case the analysis is linear elastic. However, for the more realistic theoretical methods that take into account the nonlinear behavior of the adhesive, the yield stress, the ultimate stress, and the failure strain are necessary. The stress–strain curve of adhesives is necessary for designing adhesive joints in order to compute the stress distribution and apply a suitable failure criterion based on continuum mechanics principles.

The tensile stress–strain curve on bulk specimens is generally the most common test used. This test is sufficient if the yield behavior of the adhesive is assumed to be of the von Mises type. However, it is known that adhesive yielding is better described by more complex yielding criteria (Drucker and Prager 1952; Raghava et al. 1973; Dolev and Ishai 1981) (see Chap. 23) for which an additional test under a different loading condition is required. Shear tests are usually preferred because the compressive test is more difficult to perform. There are many test methods for the determination of failure strength data. They can be divided into two main categories: tests on bulk specimens and tests in a joint or in situ. Tests in the bulk form are easy to perform and follow the standards for plastic materials. However, the thickness used should be as thin as possible to represent the thin adhesive layer present in adhesive joints. Tests in situ more closely represent reality, but there are some difficulties associated with accurately measuring the very small adhesive displacements of thin adhesive layers. Moreover, the adhesive stress distribution is not perfectly uniform, and the failure mode may not be the same as that found in real joints. Another important point is that the adhesive strength measured in a joint depends on the surface preparation. This is not only critical for the short-term strength but even more so for the long-term strength, especially if aggressive environments are present. Also, there might be a region close to the interface with chemical and physical characteristics different from those of the bulk adhesive or adherend, leading to the formation of an interphase. There has been intense debate about the most appropriate method and whether the two methods (bulk and in situ) can be related. Some argue that the properties in the bulk form may not be the same as in a joint because the cure in the bulk form and the cure in a joint (thin film) may not be identical. In effect, the adherends remove the heat produced by the exothermic reaction associated with cure and prevent overheating. However, many studies have shown that the relation is reasonable, taking into account all the differences associated with each method (Jeandrau 1991; Lilleheden 1994; da Silva and Adams 2005). The truth is that there is no perfect test for the determination of failure strength properties. The designer needs to select the most appropriate test for a given application and understand what the results mean (Adams 1990).

2 Tensile Tests

2.1 Bulk Specimens

One of the most common types of tests for determining the strength properties of adhesives is the tensile test on bulk specimens. The specimens and the test methods are comparable to those used for plastic materials. The properties determined are intrinsic to the material: they are obtained under a uniform and uniaxial state of stress, with no influence of the adherends.

The manufacture of the bulk specimen is usually done by pouring or injecting the adhesive into a mold with the final shape (Fig. 19.1 ), or by applying pressure between plates (Fig. 19.2 ). The first method is suited to one-part adhesives that are relatively liquid. The mold can be open, but it can also be a closed cavity, in which case the adhesive needs to be injected (Fig. 19.1 ). When the adhesive is viscous, in the form of a film or of two components, the second method generally gives better results. If the adhesive is viscous or in film form, the pouring (or injection) phase is difficult or impossible. On the other hand, the mixing of two-part adhesives introduces voids. If the adhesive is liquid, the air bubbles can be removed by vacuum. If the adhesive is viscous, modern sophisticated machines that allow mixing at high speed under vacuum can ensure that the adhesive is void free. If the voids have been removed properly, the adhesive can be manufactured by pouring or injection. If not, the voids can be removed by high pressures. The technique described in the French standard NF T 76-142 works particularly well for producing plate specimens without porosity. It consists of curing plates of adhesive in a mold with a silicone rubber frame under a high pressure (2 MPa or 20 atm). The pressure is calculated using the dimensions of the silicone rubber frame. The technique, shown schematically in Fig. 19.3 , consists of placing in the center part of the mold a quantity of adhesive slightly greater than the volume corresponding to the internal part of the silicone rubber frame. There is a gap, at the beginning of the cure, between the adhesive and the silicone rubber frame. At the moment of the application of the pressure, this gap enables the adhesive to flow (until the mold is completely filled) and avoids gas entrapment. This technique is suitable for any type of adhesive, i.e., liquid, paste, or film. The plates are then machined according to the dimensions used for tensile testing or for other types of geometry (see Sects. 19.3 and 19.4). The geometry generally used for tensile specimens is the dogbone shape specimen according to standard EN ISO 527-2, which is represented in Fig. 19.4 . Long specimens (Fig. 19.4a ) are used for rigid adhesives (e.g., epoxies) where the displacements are small, whereas short specimens (Fig. 19.4b ) are more suited for flexible adhesives (e.g., polyurethanes). The geometry described in ASTM D 638 (tensile properties of plastics) can also be followed. Alternatively, standard ASTM D 3039 (tensile properties of fiber–resin composites) can be used when working with supported film adhesives. It is important to specify the thickness of the plate because the adhesive properties will depend on it, especially if there are many voids in the specimen. The ideal method would be to work with very thin samples to reproduce the adhesive layer in a joint, but this is very difficult due to the high flexibility of the adhesive. Generally, a thickness of 2 mm is used; larger thicknesses can be used but the exothermic reaction during the cure can cause adhesive burning in some adhesives. Round solid bar tension specimens have also been used by some authors (Grant et al. 2009). The specimens should be conditioned under controlled temperature and humidity because these factors influence the mechanical properties of the adhesive, especially for polyurethane adhesives. This is valid for any type of test.

Fig. 19.1

Tensile bulk specimens obtained by pouring

Fig. 19.2

Bulk plates obtained by high pressure

Fig. 19.3

French method (NF T 76-142) to obtain plates without porosity (da Silva et al. 2004)

Fig. 19.4

Tensile specimens according to EN ISO 527-2 (dimensions in mm): (a) long specimen and (b) short specimen

The test consists in loading the specimen in a longitudinal direction until failure. The test speed generally used is 1 mm/min for the determination of the Young’s modulus, but higher rates can be used for failure testing. The strain rate of the adhesive measured in bulk should be similar to the strain rate the adhesive has in the joint, especially if the adhesive is close to its glass transition temperature (T _g). The temperature and humidity of the test should also be recorded. Small deviations from typical laboratory conditions (25°C and 50% relative humidity) can cause an important variation in the mechanical properties, especially if the adhesive T _g is in that range. The load and the displacement are measured, which can then be used to determine the stress–strain curve. Measurement of the adhesive displacement is relatively easy using clip gauges or strain gauges. However, whenever possible, it is recommended to use noncontacting devices to avoid any interference of the extensometer with the material behavior, especially for flexible and ductile adhesives. Optical (see Fig. 19.5 ) or laser methods are widely used. Video extensometers are not accurate enough for strains below 1%. However, other methods based on optical data treatment such as digital image correlation (DIC) enable one to measure strains below 1%. The displacement of the crosshead can also be used to estimate the adhesive strain. However, this requires a correction as the adhesive displacement in the calibrated area is not the same as that between the grips. For highly deformable adhesives, the crosshead displacement is good enough, especially for the nonlinear part of the curve.

Fig. 19.5

Adhesive displacement measurement with an optical method (da Silva et al. 2006)

A typical tensile stress–strain curve is shown in Fig. 19.6 . The stress–strain curve can be used to determine the Young’s modulus, the tensile strength, and the failure strain. There are several methods to calculate the Young’s modulus. Standard EN ISO 527-2 recommends determining the Young’s modulus between points at 0.05% and 0.25% strain. This range generally falls in the elastic range of structural adhesives. Table 19.1 shows the Young’s modulus of different types of adhesives below T _g. Stiff adhesives are in the range of 4–5 GPa (e.g., epoxies or polyaromatics). Flexible adhesives for structural use such as polyurethanes are in the range of 0.1 GPa. For flexible and ductile adhesives such as polyurethanes, the material is nonlinear even for these small deformations. Other methods such as the secant modulus or the tangent at the origin may be used. For flexible adhesives such as polyurethanes, because the displacement rate is constant, there is time for the load to relax through the test. In order to avoid this phenomenon, a test under constant strain rate should be done.

Fig. 19.6

Typical tensile stress–strain curve of an adhesive with the definition of the mechanical properties

Table 19.1 Mechanical properties of various adhesives below the glass transition temperature

The Poisson’s ratio can be determined provided the adhesive displacement is measured in the longitudinal and transversal directions. This property is very difficult to measure experimentally, especially in the elastic range. For polymers, the Poisson’s ratio varies between 0.3 and 0.5. For temperatures below the glass transition temperature (T _g), the value is close to 0.3. When the adhesive is above T _g or in the plastic region, the Poisson’s ratio is about 0.5. Table 19.1 gives the values for several adhesives. One way to determine the Poisson’s ratio is to deduce it from the measurement of the Young’s modulus and the shear modulus (see Sect. 19.5).

It is generally easy to find the yield stress of metals because there is usually a clear transition between elastic and plastic behavior. However, for polymers, the elastic region may not be linear and it is difficult to find the value of the stress corresponding to the initial yielding. Various authors have proposed methodologies to find the yield stress. Young and Lovell (1991) state that the exact position of the yield point is very difficult to estimate and so, they define yield as the maximum point on the stress–strain curve. This procedure is valid when the adhesive behaves elasto-plastically. For strain hardening adhesives, it is convenient to take the yield stress as the intersection of a line tangent to the linear elastic region and a line tangent to the nonlinear plastic region of the actual stress–strain curve, such as in the bilinear model (Hart-Smith 1973). The traditional 0.2% offset method may also be used for this effect for glassy polymers. Table 19.1 gives yield strength values for several adhesives. The strongest adhesive is in the order of 60 MPa. This is well below the yield strength of a low strength steel, which is approximately 180 MPa. However, when loaded in shear over a large area, the adhesive can deform plastically the steel.

The strain to failure is highly dependent on the presence of defects such as voids and micro-cracks. In tension, once a crack is triggered next to a void, the specimen often fails there due to the high stress concentration. Generally, the strain to failure presents a very large dispersion, unless the manufacture is very well controlled. Table 19.1 presents values of the failure strain in tension and shear. Generally, adhesives are much more ductile in shear than in tension. For ductile adhesives, the difference can be of one order of magnitude. Stiff and strong adhesives have generally a limited ductility of the order of 1% or 2%, especially in tension. On the other end of the scale, failure strains of up to 300% can be obtained with polyurethane adhesives.

2.2 Axially Loaded Butt Joints

The tensile properties can also be measured with the adhesive in a thin layer between two steel substrates as in the butt joint (also called the “poker chip” test). There are two ASTM standards for this type of test. The first, ASTM D 897, uses short circular specimens made of metal or wood, and the second (ASTM D 2095) is more general and includes round and square geometries (Fig. 19.7 ). Other standards include ISO 6922, BS EN 26922, and BS 5350 – Part C3. A mold is presented in ASTM D 2095 for controlling the adherend alignment and adhesive thickness. The stress is obtained by dividing the load by the loaded area. Apparently, the stress state is of uniform tension. However, some authors (Adams and Coppendale 1977, 1979) have shown that the stress distribution is nonuniform due to the constraining effect of the substrates or slight misalignments. The lateral contraction of the adhesive does not occur freely, which introduces additional radial and circumferential stresses, especially at the edges of the joint. In addition to the constraining effect of the substrate, misalignments can occur during fabrication or testing, which introduce bending in the adhesive.

Fig. 19.7

Butt-joint geometry (dimensions in mm) (ASTM D 2095)

The adhesive displacement can be measured by extensometers attached to the adherends, in which case a suitable correction is necessary. Taking the case illustrated in Fig. 19.8 and given by Adams et al. (1997), the extensometer displacement δ is given by

$$\eqalign{ \delta & = \delta _1 + \delta _{\rm a\,} +\delta _2 \cr & = \varepsilon _1 d_1 + \varepsilon _{\rm a} d_{\rm a} +\varepsilon _2 d_2 \cr & = \varepsilon _1 (d_1 + d_2 ) + \varepsilon_{\rm a} d_{\rm a} \cr} $$

(19.1)

where ε is the strain, and d ₁, d _a, and d ₂ are defined in Fig. 19.8 . If d ₁ and d ₂ are of the order of 1 mm and d _a (adhesive thickness) is of the order of 0.1 mm, then the displacements in the adhesive and in the adherend are of the same order. This correction is necessary for all the extensometers that measure not only the adhesive displacement but also the adherend displacement. This is a big disadvantage associated with adhesive joints and extensometers.

Fig. 19.8

Gauge length and displacements in the axially loaded butt joint

According to Adams and Coppendale (1977), the elastic properties (Young’s modulus, E, and Poisson’s ratio, ν) can still be determined using this test. They defined a relation between the “apparent” E _a measured in the test and the real E. If the substrate is infinitely rigid in relation to the adhesive, the relation between E _a and E is given by

$$ \frac{{{E_{\rm a}}}}{E} = \frac{{\left( {1 - \nu } \right)}}{{\left( {1 + \nu } \right)\left( {1 - 2\nu } \right)}} $$

(19.2)

where ν is the Poisson’s ratio of the adhesive. Another equation proposed by Kuenzi and Stevens (1963) gives the Poisson’s ratio of the adhesive, if the shear modulus of the adhesive is known, and the adherend elastic properties.

The stress–strain curve obtained with this test is not representative of the intrinsic adhesive behavior due to the adherend constraining effect described above and cannot be correlated with the adhesive bulk properties. An extensive study carried out by several laboratories and led by Centre Technologique des Industries Mécaniques from France (Jeandreau 1993) has shown that the reproducibility associated with this test is quite low, despite the use of a precise and specially designed extensometer.

3 Compressive Tests

This test is less common than the tensile or shear tests. Usually, it is assumed that the adhesive follows the von Mises model and, therefore, the compressive and tensile properties are the same. However, since adhesives depend on the hydrostatic stress component, the compressive strength properties differ from those obtained in tension. The ratio of the yield stress in compression to the yield stress in tension varies typically between 1.2 and 1.4 (Adams et al. 1997). There are various types of compressive tests on bulk specimens. The most common compressive test uses parallelepipedic (square or rectangular base) bulk specimens. The French standard NF T 51-101 recommends a square base (Fig. 19.9a ) whereas ASTM D 695 (Fig. 19.9b ) and ISO 604 use a rectangular base. In the case of ISO 604, the preferred specimens are 50 × 10 × 4 mm³ for modulus and 10 × 10 × 4 mm³ for strength. Cylinders can also be used and are 12.7 mm (1/2 in.) in diameter and 25.4 mm (1 in.) long according to ASTM D 695 (Fig. 19.10a ). Gali et al. (1981) also used tubular specimens (Fig. 19.10b ) with good results.

Fig. 19.9

Bulk specimens for compressive testing using parallelepipedic specimens (dimensions in mm): (a) according to NF T 51-101 and (b) according to ASTM D 695

Fig. 19.10

Bulk specimens for compressive properties using (dimensions in mm): (a) cylindrical (ASTM D 695) and (b) tubular specimens (Gali et al. 1981)

The specimen is placed between compressive plates parallel to the surface. The specimen is then compressed at a uniform rate. The maximum load is recorded along with stress–strain data. An extensometer attached to the front of the fixture is used to measure the adhesive displacement. The stress–strain curve is used to determine the properties of interest. Various authors have shown that the Young’s modulus in compression obtained by this method and that obtained with bulk tensile specimens correlate well. However, it is difficult to determine the failure stress and strain in compression because the adhesive keeps deforming without breaking (Jeandreau 1993).

ASTM D 695 standard also describes a procedure using a plate specimen similar to the bulk tensile test (Fig. 19.11a ). This method is valid only for rigid adhesives. However, special care must be taken to avoid buckling of the specimen, as shown in Fig. 19.11b . The machining of ends is particularly important to ensure they are smooth, flat, and parallel, with sharp and clean edges. Testing is done by placing a small specimen between the two blocks as shown in Fig. 19.11b and slowly compressing it until the point of fracture. Some of the results of this test include compressive strength, compressive yield strength, offset yield strength, and modulus of elasticity. Unpublished results by the author have shown that the values of the modulus obtained with this type of test are comparable to those obtained using the bulk tensile test. The nonlinear part of the stress–strain curve should, however, be analyzed with caution because the two blocks used to avoid buckling might stiffen the adhesive.

Fig. 19.11

Bulk specimen for compressive properties according to ASTM D 695 (dimensions in mm): (a) specimen geometry and (b) blocks to avoid specimen buckling

4 Shear Tests

As with tensile tests, shear tests can be divided into bulk and joint tests. The adhesive displacement in joint tests is very small and it is therefore more difficult to measure accurately. Bulk specimens give more accurate results because the gauge length is higher. However, it can be argued that the size and thickness of the specimens used are not representative of the adhesive properties in a joint. The National Physical Laboratory and other British laboratories (Dean et al. 1996) have carried out an extensive theoretical and experimental study on various shear test methods. Many of their findings are well accepted by the adhesive community and are also presented here.

4.1 Bulk Specimens

4.1.1 Bulk Torsion

The shear properties of the adhesive can be obtained with solid or tubular bars in torsion. The dimensions of the specimen vary from author to author. An example is given in Fig. 19.12a (Chen et al. 2011) for solid bars. The specimen manufacture depends on the type of adhesive and is described above in Sect. 19.2.1. The round shape needs to be obtained by machining, which might not be possible with very flexible adhesives. Alternatively, round specimens can be cast in a centrifuge. The square sections at the two ends are used to locate into the grips of the test machine and to transmit the torque. The round shape is free of stress concentrations and therefore the true adhesive properties can be measured with this test. The torque and the relative twist (T – φ) along the gauge length of the specimen are recorded. The shear stress τ and shear strain γ are obtained from the T – φ curve using the following equations:

$$ \tau = \frac{{Tr}}{J} $$

(19.3)

$$ \gamma = r\frac{{\phi }}{l} $$

(19.4)

where r is the radius, l is the gauge length, and J is the polar moment of inertia. Contacting extensometers are used to measure the angular rotation of a known gauge length of the specimen. The use of large gauge length enables high accuracy with this test. In case the specimen is sensitive to the extensometer, the rotation of the specimen clamps can be used. For this type of solid bar, the shear strain varies linearly along the radial direction with zero strain at the center. The shear strain at the outside surface can be derived from the measured twist. However, the stress distribution is linear only if the material is absolutely linear elastic. Nonlinear behavior is bound to occur, especially in the pure shear state. Departure from linearity will redistribute the stress in such a way that some load carried by the most-stressed material at the outside surface (in the elastic case) shifts to the material inside. The graphical correction method due to Nadai (1931) can be applied to the recorded torque–twist curve to derive the shear stress–strain response at the surface of the specimen. The correction is illustrated in Fig. 19.13 (Adams et al. 1997). A tangent to the curve is made for any point of the nonlinear part. For example, the correction to the height AB is made by subtracting one quarter of the intercept height DC, giving the corrected height AE. The relevant properties are determined from the shear stress–strain curve.

Fig. 19.12

Bulk torsion specimens (dimensions in mm): (a) solid bar torsion specimen (Chen et al. 2011) and (b) tubular specimen (Gali et al. 1981)

Fig. 19.13

Nadai correction

Tubular specimens (thin walls) can also be used and do not require a Nadai correction (Nadai 1931). The specimen geometry used by Gali et al. (1981) is presented in Fig. 19.12b . Again, relevant properties are determined from the shear stress–strain curve.

4.1.2 V-Notched Beam Shear Method (Iosipescu)

The V-notched beam shear method (or Iosipescu) and the notched plate shear method (or Arcan) are two methods of measuring the shear properties in bulk. The two methods are similar, differing only in the type of loading and geometry. Both test methods were made so that a conventional tensile testing machine can be used to apply shear. This test was originally developed for metals (Iosipescu 1967), but it has been adapted for laminated composites in the standard ASTM D 5379 following developments by Adams and Walrath (1987). The specimen is rectangular with two V-notches at its center, as shown in Fig. 19.14 . The geometry is usually 75 mm wide, 20 mm high, and at least 4 mm thick. The specimen is loaded in four points, creating an area with uniform shear between the notches since the bending moments from both sides cancel each other. Since the specimen is loaded at the edges, this can cause bending of the specimen along its longitudinal axis. To reduce this problem, thick specimens are recommended (3–4 mm). For very flexible adhesives such as polyurethanes, the testing method may not be adequate even with thick specimens. There is a stress concentration at the notch root but the shear stress calculated with the force and the cross-sectional area is a good approximation. Alternatively, a correction can be applied with a finite element (FE) analysis. For brittle adhesives, the stress concentration at the root of the notch might be sufficient to induce premature failures and give only part of the stress–strain curve. That is one of the main disadvantages of this type of test. The same thing happens with the Arcan test. The shear displacement can be measured by strain gauges mounted at +45° and −45° with the specimen axis. If P is the load applied, t the specimen thickness, and h the distance between the notches, the shear stress τ is given by

$$ \tau = \frac{P}{{th}} $$

(19.5)

and the shear modulus G by

$$ G = \frac{P}{{th\left( {{\varepsilon_{45}} - {\varepsilon_{ - 45}}} \right)}} $$

(19.6)

where ε ₄₅ and ε ₋₄₅ are the strains measured by the strain gauges bonded at +45° and −45° with the specimen axis. However, as in the tensile bulk test, strain gauges tend to stiffen the adhesive and have a limited strain limit (typically 10%). Alternatively, noncontacting devices, such as digital image correlation, can be used. The stress–strain curve can be used to determine the shear modulus, strength, and ductility.

Fig. 19.14

V-notched beam shear method (or Iosipescu) specimen dimensions (in mm) and loading

4.1.3 Notched Plate Shear Method (Arcan)

The notched plate shear method, also called Arcan, is used to obtain the shear properties on bulk specimens. The specimen geometry looks like a butterfly (Fig. 19.15 ) and the test is also known as the butterfly test (Voloshin and Arcan 1980). The specimen contains two symmetric notches at 90° with a radius of curvature of 1.5 mm to minimize the stress concentration. The holes on the sides of the specimen allow the application of a shear loading (Fig. 19.16 ) that is uniform between the two notches. This loading arrangement avoids the problem of instability at the edges that occurs in the Iosipescu test and enables to work with thinner specimens. This is useful for flexible adhesives or for adhesives that have a big exothermic reaction during cure. There are, however, stress concentrations near the notches that can induce premature failures, especially for brittle adhesives (Dean et al. 1996). The stress is obtained dividing the load by the resistant area between the two notches. The displacement in the uniform shear deformation zone between the two notches can be measured with extensometers mounted on the specimen, with strain gauges bonded at +45° and −45° with the loading axis, or with noncontacting methods (Pinto et al. 2010). Dean et al. (1996) have developed an extensometer that is mounted on the specimen and which consists of a pair of levers and displacement transducers. The extensometer is fixed to the grips and contacts the specimen at two points near the specimen center. For large strains (typically 20%), instabilities due to the loading arrangement make the results unreliable.

Fig. 19.15

Notched plate shear method (or Arcan or butterfly) (dimensions in mm)

Fig. 19.16

Loading jig of the Arcan specimen

Arcan et al. (1978) proposed a biaxial fixture, commonly known as the Arcan fixture, to produce biaxial states of stress. The compact nature of the Arcan fixture enables obtaining the shear properties in all in-plane directions in a relatively simple manner. The Arcan fixture can be used to apply both shear and axial forces to the test specimen. The adhesive characterization in mixed mode loading allows for the generation of the yield surface of the adhesive in the hydrostatic versus the von Mises plane, which enables one to develop more accurate adhesive models for better simulations. Several modifications to the original test fixture have been proposed to include compression, such as that by El-Hajjar and Haj-Ali (2004). A scheme of the test fixture is shown in Fig. 19.17 .

Fig. 19.17

Modified Arcan fixture for mixed loading

4.2 Joint Specimens

One can argue that the adhesive properties measured in a joint are more representative. Furthermore, the fabrication and testing procedure is relatively simple, especially for the case of the thick adherend shear test (TAST). However, the main disadvantage is the need for high-precision measurement devices due to the low adhesive displacements. In many cases, extensometers that measure both adherend and adhesive displacements are used, which means that a correction is necessary to remove the adherend displacement. Another feature common to all joint tests is the fact that for a constant test speed, the strain rate in the adhesive will increase when the adhesive deforms plastically, which will increase the yield stress of the adhesive compared to a test carried out under constant strain rate.

4.2.1 Arcan and Iosipescu Joint Methods

The Arcan and Iosipescu specimens can also be used as a joint where the adhesive is in a thin layer between two substrates. The test methodology is very similar to the bulk version. The adhesive displacement can be measured by noncontacting devices or extensometers of the type proposed by Dean et al. (1996). For devices that measure the adhesive and adherend displacement, a correction must be applied to have only the adhesive displacement. The stress distribution is not perfectly uniform, and an FE analysis can be used to have the value at the center of the specimen where the strain is obtained. Grabovac and Morris (1991) and Wycherley et al. (1990) used the Iosipescu method where two shaped adherends are bonded together. Weissberg and Arcan (1988) proposed a joint test based on the Arcan configuration. More recently, Cognard et al. (2005) proposed an Arcan joint method to produce not only shear but also biaxial stress states.

4.2.2 Butt Joint in Torsion

The butt joint with solid substrates or tubes can be used. The geometry of the specimen is represented in Fig. 19.18 for the butt joint with solid substrates (Adams and Coppendale 1977). As in the bulk torsion method, this test is free of stress concentrations, which enables having larger strain to failures than other types of tests where stress concentrations exist. Also, the adhesive displacement generated is higher, which gives a higher accuracy for the strain than other joint methods. If the same dimensions are used as the bulk torsion test, the same test apparatus can be used. Contacting extensometers used for the bulk torsion test are also applicable to the butt joint, but a correction is needed to remove the displacement of the substrates, especially if the adhesive is strong and stiff (Adams et al. 1997). As in the bulk torsion test, the shear stress–strain curve obtained must also be corrected as in the bulk torsion method (Nadai 1931). The manufacture can be difficult when an adhesive of low viscosity is used because it is difficult to fill the bonded area properly. Adams and Coppendale (1977) designed a jig to produce fully filled joints with low viscosity adhesives.

Fig. 19.18

Butt joint in torsion with solid adherends (dimensions in mm) (Adams and Coppendale 1977)

Another type of butt-joint test in torsion is the napkin ring where the adhesive is in a thin layer between two tubular substrates. ASTM E 229, ISO 11003-1, and DIN 54451 describe this method (Fig. 19.19 ). Because tubes are used, the adhesive is essentially at the same shear stress, since the shear stress is proportional to the radius r (see Eq. (19.3). Althof and Neumann (1974) have shown that the napkin-ring test and the thick adherend shear test (see Sect. 19.4.2.3) give a very similar shear stress–strain curve. The main disadvantage of this type of test is the difficulty of manufacture. In case the adhesive has low viscosity, the manufacture is particularly difficult because the adhesive will not stay in position. In the napkin-ring test, the adhesive fillets inside and outside should be removed because they make the calculation of the shear strength and modulus less exact. The outer fillet is easy to remove. However, the inner fillet is impossible to clean away. If the thickness of the tubes is thin enough, the effect of the fillet can be neglected.

Fig. 19.19

Napkin-ring test specimen

4.2.3 Thick Adherend Shear Test

The thick adherend shear test (TAST) is one of the most popular types of failure strength test because it is easy to make and test the specimens. Shear properties obtained with this test are presented in Table 19.1 . The conventional single lap shear joint, which is mostly used for comparison and quality control of adhesives, puts the adhesive in a complicated state of stress (see Sect. 19.4.2.4). Therefore, it is not suitable for the determination of the true adhesive properties. When stiff and thick metallic adherends are used, the adhesive is in a state of essentially uniform shear over most of the overlap, and peel stresses are reduced. Two forms of the TAST are used, as developed by Krieger (1988) (ASTM D 3983), in the USA, and Althof and Neumann (1974) (ISO 11003-2), in Europe. The main difference between the two tests is the size of the specimen: the Althof specimen is half the size of Krieger’s. They both developed extensometers for measuring the very small displacements across the bondline (Fig. 19.20 ). The extensometer measures not only the displacement of the adhesive, but also the displacement of the adherend (Fig. 19.21 ). Therefore, it is necessary to apply a correction to the measured displacements. According to ISO 11003-2, the correction should be deduced from the measurement of the shear strain on a “dummy” specimen consisting of the adherend material alone. Vaughn (1998) modeled the TAST specimen and the “dummy” specimen. The predicted profile of shear stress along the centerline of the adhesive is almost constant. Conversely, the shear stress distribution in the “dummy” is not uniform, so the correction cannot be deduced from that specimen. As part of a project to evaluate the relative performance of shear tests, Vaughn (1998) suggests that the adherend correction can be derived from simple elasticity assuming that the adherends experience pure shear only:

$$\eqalign{ & d_{{\mathop{\rm adhesive}\nolimits} } = d_{\rm transducer} - 2 \times d_{{\mathop{\rm adherend}\nolimits} } \cr & 2 \times d_{{\mathop{\rm adherend}\nolimits} } = {{2 \times t_{{\mathop{\rm adherend}\nolimits} } \times P} \over {G_{{\mathop{\rm adherend}\nolimits} } \times l \times w}} \cr & 2 \times t_{\rm adherend} = 3.8{\rm mm} - t_{\rm adhesive} \cr} $$

(19.7)

where d is the thickness (mm), P the load (N), G the shear modulus (MPa), l the length of the overlap (5 mm), and w the width (25 mm). However, an FE analysis shows that direct axial stress is also carried by the adherend. Thus, an accurate correction cannot be properly calculated assuming that the adherends experience only pure shear. Taking this into account, it is better to use an FE analysis correction. Nevertheless, a simple elasticity correction is shown to be acceptable as long as the adhesive thickness is not too small. The adhesive displacement can also be measured with a conventional clip gauge used for tensile testing (da Silva et al. 2008). However, a correction is also needed. Optical methods such as image correlation analysis are probably the best because they give the adhesive displacement directly and do not interfere with the adhesive behavior (Pinto et al. 2010).

Fig. 19.20

Thick adherend shear test (TAST) extensometer

Fig. 19.21

Thick adherend shear test (TAST) transducer measured displacement

Despite the almost uniform stress distribution in the adhesive, stress concentrations still exist, especially at the edges of the overlap close to the interface. Several researchers have proposed modifications of the TAST geometry to reduce these effects, including Lilleheden (1994) and Cognard et al. (2008), who propose the use of specially shaped adherends to reduce these stress concentrations. However, the machining cost is quite substantial. Another alternative is to use a spew fillet to reduce stress concentration, which avoids premature failures and enables the determination of the maximum of the stress–strain curve.

As regards the specimen manufacture, ISO 11003-2 recommends machining the specimens from two plates bonded together. However, this technique has disadvantages such as the effect of cutting in the highly stressed region at the end of the adhesive layer where initial failure is likely to occur. Vaughn (1998) proposed that a better solution was to machine the adherends to the correct dimensions before bonding (Fig. 19.22 ). The bending stiffness is higher than when the joint is composed of two bonded bars and, therefore, reduces the peel stresses. A specially built jig was designed for aligning and holding the specimens. To control the overlap and fillet, steel shims were inserted into the gaps once the adherends were brought together.

Fig. 19.22

Thick adherend shear test (TAST) (dimensions in mm)

The test speed recommended by the standard ISO 11003-2 is 0.5 mm/min. However, a constant crosshead displacement rate will induce an accelerating strain rate in the adhesive once it starts yielding, influencing the yielding properties. This is a common feature of all the joint tests, contrarily to the bulk tests where the strain rate is much more constant for a given crosshead rate. To have a constant adhesive strain rate, the crosshead speed can be controlled using the adhesive displacement measurements.

4.2.4 Tests with Thin Sheet Adherends

Tests with thin sheet adherends, and in particular the single lap joint (SLJ) test, are very common in the industry. This has to do with the fact that it reproduces joints encountered in aeronautical structures that were the pioneers of adhesive bonding technology. The SLJ is described in ASTM D 1002 and ISO 4587. The usual dimensions are indicated in Fig. 19.23a . These standards recommend cutting specimens from two bonded plates 178 mm (7 in.) wide. However, the joints can be made individually in a mold, reducing the defects introduced by cutting. As seen in Part E, the SLJ is in a complex state of stress. Due to the load misalignment, even if tab ends are used, and due to the differential adhesive straining effect (Volkersen 1938), the adhesive is subjected to a state of nonuniform shear and peel stresses (see Fig. 19.23b and c ). Nevertheless, the ASTM D 1002 standard recommends reporting the results as the average shear stress at failure (maximum load divided by bond area). It is important to choose adherends that do not yield prior to joint failure. Otherwise, what causes the failure of the joint is the yielding of the adherend. In other words, the yielding of the adherend is being measured and not the actual strength of the adhesive.

Fig. 19.23

Single lap joint: (a) dimensions in mm (ASTM D 1002); (b) adhesive shear stress distribution along the overlap; and (c) adhesive peel stress distribution along the overlap

The SLJ has the advantage of being simple and cheap. It is widely used and gives an idea of the adhesive shear strength. Valuable information is contained in the lap shear strength. The lap shear strength depends, among other things, on the yield strength of the adherends and the overlap length as shown schematically in Fig. 19.24 . For the mild steel adherends, as the overlap increases there is some increase in strength, but a plateau is reached quickly. In this case, the plastic deformation of the mild steel controls failure. As for the hard steel, the adherends remain elastic and the strength increases almost linearly as the overlap increases, especially if the adhesive is ductile. An interesting result is that the slope of the tangent to the curves (as indicated in Fig. 19.24 ) gives a shear strength (τ = load/(overlap length × joint width)) equal to the maximum shear stress given by a shear stress–shear strain curve. Therefore, the lap shear strength gives an approximate value of the shear strength of the adhesive, provided high-strength adherends are used (with no yield) (Banea and da Silva 2009). Another factor that should be taken into account is the adhesive thickness. It has been shown experimentally by many authors that the joint strength decreases as the adhesive thickness increases. Also, the effective strain rate at constant displacement rate is affected by adhesive thickness. Therefore, it is important to indicate the adhesive thickness used. This is valid for all the joint tests. For relatively thin values (0.1–0.4 mm), the SLJ strength variation is not substantial (Adams and Peppiatt 1974, da Silva et al. 2006). The SLJ test does not give the shear strain at failure. The adhesive must be tested in uniform shear to obtain the shear stress–shear strain curve.

Fig. 19.24

Lap shear strength versus overlap strength

Other tests with thin sheet adherends have been used to have a more uniform adhesive stress distribution along the overlap, such as the laminated joint shown in Fig. 19.25a according to ASTM D 3165. The bending moment is largely reduced but the differential straining is still present. The double lap joint (Fig. 19.25b ) also reduces the peel stresses due to the alignment of the load. Internal bending effects in the joint cause peel stresses at the ends of the internal adherend. Another type of double lap joint, also called double strap joint, can be used. Here again, despite the reduction of the peel stresses, the adhesive shear stress is still not uniform due to the differential straining effect.

Fig. 19.25

(a) Laminated joint (ASTM D 3165) and (b) double lap joint with stress distribution (ASTM D 3528) (dimensions in mm)

4.2.5 Pin-and-Collar Test

Standards ASTM D 4562 and ISO 10123 describe a shear test in which the specimen is a pin bonded inside a collar. The test uses a press to force the pin through the collar, which rests on a support cylinder. The test results are the load required to initiate failure divided by the bonded area between the pin and the collar. This type of test is particularly suited to test anaerobic adhesives. The shear strength determined with this test is only an average value because the stress distribution is not uniform along the overlap (Nemeş et al. 2006; Martínez et al. 2008). ASTM E 229 also uses a pin-and-collar type of specimen except that here torsional loadings cause failure. The adhesive stress distribution in this case is more uniform and may be used to determine the adhesive shear modulus and strength. However, the standard was withdrawn in 2003.

4.3 Recommendations

The most recent literature shows that all the test methods described above do not show a systematic variability in the shear stress–strain curves (Althof and Neumann 1974; Jeandreau 1993; Dean et al. 1996; da Silva and Adams 2005). The differences can be attributed to materials variability and different precision associated with each test method and manufacture.

The test that offers the most accuracy is the bulk torsion test in case of bulk specimens and the butt joint in torsion for the joint tests. However, torsion devices are not common in most laboratories. The bulk torsion specimen is also limited to adhesives that are sufficiently rigid to be machined. For example, it is not applicable to a silicone or a polyurethane.

In case a torsion machine is not available, the TAST is probably the simplest and most reliable technique to use. The Arcan joint is also a good alternative and is easily adaptable to mixed loading, which is very important for the proper adhesive yielding failure envelope.

5 Relation Between Tensile, Compressive, and Shear Properties

As described above, there is a wide range of test methods available and it is difficult to make the right choice. However, the properties obtained in compression, tension, and shear can be related. One of the objectives of the adhesive characterization is to generate test data for constitutive modeling. If a von Mises–type criterion is used, then only one type of test is sufficient. Generally, in such a case, the bulk tensile test or the TAST is used. But other tests such as the bulk torsion test can also be used. However, if a more refined yielding model is used such as that of Dolev and Ishai (1981), then the properties of the adhesive in at least two loading modes are necessary. In this case, the tests generally chosen are the bulk tensile test and the TAST. Various authors have shown that the elastic properties obtained by each method correlate reasonably well. For a homogeneous material, the relation between the Young’s modulus E and the shear modulus G is

$$ E = \frac{G}{{2\left( {1 + \nu } \right)}} $$

(19.8)

where ν is the Poisson’s ratio. If E is taken from the bulk tensile test and G from a shear test such as the TAST, values of ν between 0.3 and 0.5 are obtained for most adhesives (Lilleheden 1994; Dolev and Ishai 1981; Jeandrau 1991; da Silva and Adams 2005). Figure 19.26 shows on the same graph three stress–strain curves obtained by compression on bulk specimens (ASTM D 695), tension on bulk specimens (EN ISO 527-2), and shear using the TAST (ISO 11003-2). The predicted shear stress–strain using a modified von Mises model (Dolev and Ishai 1981) curve from the compressive and tensile results is also shown. The agreement with the experimental shear curve is very good. However, if the shear stress–strain curve of the same epoxy adhesive were to be predicted using the conventional von Mises model, then the predicted curve would be below the experimental one (also shown in Fig. 19.26 ). Adhesive properties in tension, compression, and shear are therefore well correlated provided a model that takes into account the hydrostatic stress component is used. However, the prediction of the shear strain to failure does not compare well with the experimental value. The shear strain to failure is the most difficult parameter to obtain in terms of both accuracy and precision. It is highly dependent on the type of loading and the quality of the specimen. The adhesive has a different behavior when loaded in shear and in tension in the presence of defects such as voids. In tension, once a crack is triggered next to a void, the specimen fails due to the high stress concentration. In shear, even if a crack is triggered, the remaining area is capable of further deformation, especially if the adhesive is ductile. For example, in bulk tension, a small void will cause a premature failure whereas in the TAST, the presence of a void is not as critical. There have been recent advances in this area where the same type of specimen is used for all loadings giving very good results up to the failure strain (Cognard et al. 2010).

Fig. 19.26

Basic stress–strain data curves under uniaxial loading in tension and compression and under shear for an epoxy adhesive

6 Conclusions

This chapter describes the major failure strength tests used to determine intrinsic adhesive properties. Tensile, compressive, and shear tests are described with reference to major international standards. Bulk and in situ (adhesive in a joint) tests are discussed and related. The major conclusions that can be drawn are the following:

• 1. The elastic properties can be determined by any test except tests with thin adherends or the pin-and-collar test.

• 2. In tension, the recommended test is the bulk tensile test. The axially loaded butt joint has poor repeatability and suffers from constraining effects.

• 3. Compressive tests are, in general, difficult to perform and little data exists in the literature. Bulk specimens are commonly used, but the failure stress and strain are difficult to measure.

• 4. There is a wide variety of shear tests. All the test methods described in this chapter do not show a systematic difference in the shear stress–strain curves. Torsion tests are the most accurate. However, torsion devices are not common in most laboratories. In case a torsion machine is not available, the TAST is probably the simplest and most reliable technique to use.

• 5. Adhesive properties (except the strain to failure) in tension, compression, and shear can be correlated, provided a model that takes into account the hydrostatic stress component is used.

• 6. The shear strain to failure is the most difficult parameter to obtain in terms of both accuracy and precision. It is highly dependent on the type of loading and the quality of the specimen.

• 7. Devices based on Arcan and TAST geometries are being developed that can apply mixed loadings to the same type of specimen. The results obtained show that even the strain to failure can be related.